Bayesian activity detection and channel estimation with consistent sparsity in grant-free access

Abstract

The unprecedented development of Internet of Things has introduced new technological requirements for 5G and 6G communications to support massive devices with sporadic data packets. Grant-free random access has therefore been designed to enable devices to transmit data without requesting permission from base stations (BSs), significantly reducing latency and signaling overhead. Without coordination from BSs, joint activity detection and channel estimation (JADCE) become critical for subsequent data decoding. This task, given the intermittency of devices' activity, can be formulated as a compressed sensing problem.

Despite advances in Bayesian and non-Bayesian methods for JADCE, three major research gaps persist. Firstly, existing algorithms mostly require precise knowledge of system parameters, which in practice need to be estimated. Not only would this consume extra signaling overhead, estimation errors are also inevitable, leading to performance degradation. Secondly, in a popular class of approximate message passing (AMP)-based methods, consistent sparsity patterns among different antennas and access points in cell-free systems are not efficiently utilized. This leaves an impression that AMP-based methods are inferior to the dominant covariance-based approach of this area. Thirdly, existing approaches mostly rely on Gaussian channel models, and are difficult to extend to non-Gaussian channels, making existing methods not applicable to many emerging wireless communication scenarios. To this end, this thesis investigates joint activity status and system parameters estimation from a Bayesian perspective, and shows that the above-mentioned research gaps can be resolved with proper modeling and inference algorithms.

Specifically, in the first part of this thesis, a sparsity-enforcing generalized hyperbolic prior with high flexibility is employed on the combined device activity status and large-scale fading coefficients to all access points. Based on this model, a maximum a posteriori algorithm and a variational inference algorithm are derived. The proposed methods represent the first systematic study on JADCE under inaccurate system parameter information.

The second part of this thesis investigates AMP-based JADCE with a consistent activity status for each device. Based on the Bernoulli-Gaussian model but modified with a consistent activity status governing all the associated channels of each device, an AMP-based expectation-maximization algorithm is derived to estimate device activity statuses and channels. It is proved theoretically that under mild conditions, ground-truth activity status recovery is guaranteed. To further detach the reliance on long pilot sequences, a vector AMP-based algorithm is also proposed. Simulation results show, for the first time, the AMP-based method with a proper consistency modeling, could outperform covariance-based methods in cell-free systems.

Finally, the third part of the thesis investigates the combination of consistent sparsity and non-Gaussian distributed channels in intelligent reflecting surface (IRS)-assisted systems. A variance-gamma channel model is built based on accurate statistics of composite device-IRS-BS channels and further incorporated with Bernoulli distributions in which a consistent activity probability is assigned to each device. An expectation-maximization extension of AMP is derived to estimate activity probabilities and device-IRS-BS channels. Simulation results show superior performance of the variance-gamma model over a large range of IRS sizes and the consistent activity probability improves detection accuracy by over tenfold.